Kinetic Energy Calculator
Find kinetic energy from mass and speed, or find the mass or speed from kinetic energy, with units in joules, kJ and foot-pounds.
Results
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Steps
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Quick Answer
Kinetic energy is the energy of motion: KE = ½ × m × v², with mass in kilograms and speed in meters per second. A 1,500 kg car at 20 m/s (72 km/h, about 45 mph) has ½ × 1,500 × 20² = 300,000 joules, or 300 kJ.
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Table of Contents
- Kinetic Energy Calculator
- Quick Answer
- Related Calculators
- How This Kinetic Energy Calculator Works
- How to Use the Kinetic Energy Calculator
- Core Formulas
- Key Terms
- Worked Example
- Real-Life Examples
- Kinetic Energy vs Potential Energy
- Kinetic Energy of a 1,500 kg Car
- Why Speed Matters So Much
- Common Mistakes to Avoid
- Frequently Asked Questions
- References & Sources
How This Kinetic Energy Calculator Works
Choose what you want to find, then enter the other two values with their units. The calculator converts mass to kilograms and speed to meters per second, applies the formula, and shows the answer in joules, kilojoules and foot-pounds.
Quick explanation: KE = ½mv². Doubling speed makes kinetic energy four times larger.
- Mass: kg, g or lb.
- Speed: m/s, km/h or mph.
- Energy: joules (J), the SI unit.
How to Use the Kinetic Energy Calculator
- Choose whether to find kinetic energy, mass or speed.
- Enter the two values you know.
- Choose the units for mass and speed.
- Press Calculate.
- Read the answer in several units, with the steps.
Core Formulas
- Kinetic energy: KE = ½ × m × v²
- Mass: m = 2 × KE ÷ v²
- Speed: v = √(2 × KE ÷ m)
- Units: 1 J = 1 kg·m²/s² ≈ 0.7376 ft·lbf
Key Terms
- Kinetic energy: the energy an object has because it is moving.
- Joule (J): the SI unit of energy, equal to 1 kg·m²/s².
- Mass: the amount of matter in an object, in kilograms.
- Velocity: speed in a given direction.
- Work-energy theorem: the work done on an object equals its change in kinetic energy.
Worked Example
A baseball of 0.145 kg is thrown at 40 m/s (about 90 mph).
- KE = ½ × 0.145 × 40²
- = 0.5 × 0.145 × 1,600
- = 116 J
Real-Life Examples
- Car speeds: a 1,500 kg car has 134.9 kJ at 30 mph and 539.6 kJ at 60 mph, four times as much.
- Cycling: a rider and bike of 90 kg at 25 km/h have about 2,170 J.
- A dropped phone: a 0.2 kg phone hitting the ground at 5 m/s has 2.5 J.
- A running person: 70 kg at 5 m/s has 875 J.
- A wind turbine: the moving air that passes through the blades each second carries kinetic energy, which the turbine turns into electricity.
Kinetic Energy vs Potential Energy
- Kinetic energy: energy of motion, ½mv².
- Potential energy: stored energy from position, such as height: m × g × h.
- They swap: a falling object turns potential energy into kinetic energy.
- Example: a 1 kg ball dropped from 10 m reaches about 98 J of kinetic energy, ignoring air.
Kinetic Energy of a 1,500 kg Car
| Speed (mph) | Speed (m/s) | Kinetic energy (kJ) |
|---|---|---|
| 10 | 4.47 | 15.0 |
| 20 | 8.94 | 60.0 |
| 30 | 13.41 | 134.9 |
| 40 | 17.88 | 239.8 |
| 50 | 22.35 | 374.7 |
| 60 | 26.82 | 539.6 |
| 70 | 31.29 | 734.4 |
| 80 | 35.76 | 959.3 |
Why Speed Matters So Much
- Squared speed: energy grows with the square of speed.
- Road safety: a car at 60 mph has four times the energy it has at 30 mph, which is why crashes at speed are so much worse.
- Braking distance: brakes must remove all of that energy, so stopping distances rise sharply with speed.
- Mass: doubling mass only doubles the energy.
Common Mistakes to Avoid
- Forgetting to square the speed. v² matters most in the formula.
- Using km/h or mph directly. Convert to m/s for an answer in joules.
- Using grams. Convert grams to kilograms first.
- Leaving out the ½. KE is half of m × v².
- Using weight instead of mass. Use mass in kilograms, not force in newtons.
Frequently Asked Questions
KE = ½ × m × v², with mass in kg and speed in m/s.
Joules (J). Other units include kilojoules and foot-pounds.
It becomes four times larger, because speed is squared.
No. Mass is positive and speed squared is never negative.
Use v = √(2 × KE ÷ m).
No. It has size but no direction, so it is a scalar.
Multiply joules by about 0.7376.
The work done on an object equals the change in its kinetic energy. To stop a moving car, the brakes must do work equal to all its kinetic energy.
It turns into other forms, mostly heat, along with some sound and changes in shape, such as in a crash.
The energy of a spinning object, such as a wheel. It uses ½ × I × ω², where I is the moment of inertia and ω is the spin rate.
It varies widely by bullet and speed. Enter the mass and speed here to find the value for a specific case.
No. Moving north or south at the same speed gives the same kinetic energy.
Not always. A light object moving very fast can have more energy than a heavy, slow one.
References & Sources
| Source | Used For | Link |
|---|---|---|
| Wikipedia, Kinetic energy | Definition and formulas. | https://en.wikipedia.org/wiki/Kinetic_energy |
| NIST, SI units | The joule and other SI units. | https://www.nist.gov/pml/owm/metric-si/si-units |